The elongation of a planet is the angle formed by the planet

The elongation of a planet is the angle formed by the planet, earth, and sun (see the figure). When Venus achieves its maximum elongation of 46.3°, the earth, Venus, and the sun form a triangle with a right angle at Venus. Find the distance between Venus and the sun in astronomical units (AU). (By definition the distance between the earth and the sun is 1 AU.) (Round your answer to three decimal places.)

Solution

Given that:
venus, earth and sun form a right triangle
with the earth-sun segment as the hypotenuse or length = 1
and the venus-sun segment as the side opposite the angle 46.3°
so
sin(46.3°) = opposite/hypotenuse =1/hypotenuse
hypotenuse=1*sin(46.3°)=0.7229
which means the distance of venus to the sun is:
approx. 0.723 AU